Quasi-recurrent neural network

ABSTRACT

The technology disclosed provides a quasi-recurrent neural network (QRNN) that alternates convolutional layers, which apply in parallel across timesteps, and minimalist recurrent pooling layers that apply in parallel across feature dimensions.

CROSS REFERENCE TO OTHER APPLICATIONS

This application claims the benefit of U.S. Provisional Patent Application 62/417,333, “QUASI-RECURRENT NEURAL NETWORKS” (Atty. Docket No. SALE 1180-1/1946PROV), filed on Nov. 4, 2016. The priority provisional application is hereby incorporated by reference;

This application claims the benefit of U.S. Provisional Patent Application 62/418,075, “QUASI-RECURRENT NEURAL NETWORKS” (Atty. Docket No. SALE 1180-2/1946PROV2), filed on Nov. 4, 2016. The priority provisional application is hereby incorporated by reference; and

This application incorporates by reference US Nonprovisional Patent Application entitled “QUASI-RECURRENT NEURAL NETWORK BASED ENCODER-DECODER MODEL” (Atty. Docket No. SALE 1180-4/1946US2), filed contemporaneously herewith.

FIELD OF THE TECHNOLOGY DISCLOSED

The technology disclosed relates generally to natural language processing (NLP) using deep neural networks, and in particular relates to a quasi-recurrent neural network (QRNN) that increases computational efficiency in NLP tasks.

BACKGROUND

The subject matter discussed in this section should not be assumed to be prior art merely as a result of its mention in this section. Similarly, a problem mentioned in this section or associated with the subject matter provided as background should not be assumed to have been previously recognized in the prior art. The subject matter in this section merely represents different approaches, which in and of themselves can also correspond to implementations of the claimed technology.

Recurrent neural networks (RNNs) are a powerful tool for modeling sequential data, but the dependence of each timestep's computation on the previous timestep's output limits parallelism and makes RNNs unwieldy for very long sequences. The technology disclosed provides a quasi-recurrent neural network (QRNN) that alternates convolutional layers, which apply in parallel across timesteps, and minimalist recurrent pooling layers that apply in parallel across feature dimensions.

Despite lacking trainable recurrent layers, stacked QRNNs have better predictive accuracy than stacked LSTMs of the same hidden size. Due to their increased parallelism, they are up to 16 times faster at train and test time. Experiments on language modeling, sentiment classification, and character-level neural machine translation demonstrate these advantages and underline the viability of QRNNs as a basic building block for a variety of sequence tasks.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to like parts throughout the different views. Also, the drawings are not necessarily to scale, with an emphasis instead generally being placed upon illustrating the principles of the technology disclosed. In the following description, various implementations of the technology disclosed are described with reference to the following drawings, in which:

FIG. 1 illustrates aspects of a quasi-recurrent neural network (QRNN) that increases computational efficiency in natural language processing (NLP) tasks.

FIG. 2 shows one implementation of a convolutional layer that operates in parallel over a time series of input vectors and concurrently outputs convolutional vectors.

FIG. 3 depicts one implementation of a convolutional vector comprising an activation vector, a forget gate vector, an input gate vector, and an output gate vector.

FIG. 4 is one implementation of multiple convolutional vectors, and comprising activation vectors and gate vectors, concurrently outputted by a convolutional layer.

FIG. 5 illustrates one implementation of feature values at ordinal positions in activation vectors and gate vectors concurrently outputted by a convolutional layer.

FIG. 6 is one implementation of a single-gate pooling layer that applies accumulators in parallel to concurrently accumulate an ordered set of feature sums in a state vector, and sequentially outputs successive state vectors.

FIG. 7 illustrates one implementation a multi-gate pooling layer that applies accumulators in parallel to concurrently accumulate an ordered set of feature sums in a state vector, and sequentially outputs successive state vectors.

FIG. 8 depicts one implementation of successive state vectors sequentially outputted by a pooling layer.

FIG. 9 is one implementation of a QRNN encoder-decoder model.

FIG. 10 is a table that shows accuracy comparison of the QRNN on sentiment classification task.

FIG. 11 shows one implementation of visualization of QRNN's state vectors.

FIG. 12 depicts a table that shows accuracy comparison of the QRNN on language modeling task.

FIG. 13 is a table that shows accuracy comparison of the QRNN on language translation task.

FIG. 14 depicts charts that show training speed and inference speed of the QRNN.

FIG. 15 is a simplified block diagram of a computer system that can be used to implement the QRNN.

DETAILED DESCRIPTION

The following discussion is presented to enable any person skilled in the art to make and use the technology disclosed, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed implementations will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other implementations and applications without departing from the spirit and scope of the technology disclosed. Thus, the technology disclosed is not intended to be limited to the implementations shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.

The discussion is organized as follows. First, an introduction describing some of the problems addressed by the QRNN is presented. Then, the convolutional layer that implements timestep-wise parallelism is described, followed by the pooling layer that implements feature dimension-wise parallelism. Next, the QRNN encoder-decoder model is discussed. Lastly, some experimental results illustrating performance of the QRNN on various NLP tasks are provided.

Introduction

Recurrent neural networks (RNNs), including gated variants such as the long short-term memory (LSTM) have become the standard model architecture for deep learning approaches to sequence modeling tasks. RNNs repeatedly apply a function with trainable parameters to a hidden state.

Recurrent layers can also be stacked, increasing network depth, representational power and often accuracy. RNN applications in the natural language domain range from sentence classification to word-level and character-level language modeling. RNNs are also commonly the basic building block for more complex models for tasks such as machine translation or question answering.

In RNNs, computation at each timestep depends on the results from the previous timestep. Due to this reason, RNNs, including LSTMs, are limited in their capability to handle tasks involving very long sequences, such as document classification or character-level machine translation, as the computation of features or states for different parts of the document cannot occur in parallel.

Convolutional neural networks (CNNs), though more popular on tasks involving image data, have also been applied to sequence encoding tasks. Such models apply time-invariant filter functions in parallel to windows along the input sequence. CNNs possess several advantages over recurrent models, including increased parallelism and better scaling to long sequences such as those often seen with character-level language data. Convolutional models for sequence processing have been more successful when combined with RNN layers in a hybrid architecture because traditional max-pooling and average-pooling approaches to combining convolutional features across timesteps assume time invariance and hence cannot make full use of large-scale sequence order information.

The technology disclosed provides a quasi-recurrent neural network (QRNN) that addresses drawbacks of standard models like RNNs and CNNs. QRNNs allow for parallel computation across both timesteps and feature dimensions, enabling high throughput and good scaling to long sequences. Like RNNs, QRNNs allow the output to depend on the overall order of elements in the sequence. QRNNs are tailored to several natural language tasks, including document-level sentiment classification, language modeling, and character-level machine translation. QRNNs outperform strong LSTM baselines on all three tasks while dramatically reducing computation time.

Intuitively, many aspects of the semantics of long sequences are context-invariant and can be computed in parallel (e.g., convolutionally), but some aspects require long-distance context and must be computed recurrently. Many existing neural network architectures either fail to take advantage of the contextual information or fail to take advantage of the parallelism. QRNNs exploit both parallelism and context, exhibiting advantages from both convolutional and recurrent neural networks. QRNNs have better predictive accuracy than LSTM-based models of equal hidden size, even though they use fewer parameters and run substantially faster.

Experiments show that the speed and accuracy advantages remain consistent across tasks and at both word and character levels. Extensions to both CNNs and RNNs are directly applicable to the QRNN, while the model's hidden states are more interpretable than those of other recurrent architectures as its channels maintain their independence across timesteps. Therefore, an opportunity arises for the QRNNs to serve as a building block for long-sequence tasks that were previously impractical with traditional RNNs.

Quasi-Recurrent Neural Network (QRNN)

FIG. 1 shows the computation structure of a QRNN 100. QRNN 100 contains two kinds of components or layers, namely, convolutional layers (like 102, 106) and pooling layers (like 104, 108). The convolutional layers 102, 106 allow fully parallel computation across sequence minibatches and timesteps. The pooling layers 104, 108 lack trainable parameters and apply fully parallel computation across sequence minibatches and feature dimensions. In FIG. 1, the continuous blocks of the pooling layers 104, 108 indicate parameterless functions that operate in parallel along the feature dimensions.

FIG. 1 also shows sub-QRNNs 110, 112. Sub-QRNN 110 contains at least one convolutional layer 102 and at least one pooling layer 104. Sub-QRNN 112 contains at least one convolutional layer 106 and at least one pooling layer 108. In other implementations, each of the sub-QRNNs 110, 112 include any number of convolutional layers (e.g., two, three, or more) and any number of pooling layers (e.g., two, three, or more). Also in other implementations, QRNN 100 can include one or more sub-QRNNs.

In some implementations, QRNN 100 contains a sequence of sub-QRNNs arranged from a lowest sub-QRNN in the sequence to a highest sub-QRNN in the sequence. As used herein, a QRNN with multiple sub-QRNNs arranged in a sequence is referred to as a “stacked QRNN”. A stacked QRNN, such as QRNN 100, processes received input data through each of the sub-QRNNs in the sequence to generate an alternative representation of the input data. In addition, the sub-QRNNs, such as sub-QRNNs 110, 112, receive, as input, a preceding output generated by a preceding sub-QRNN in the sequence. For example, in FIG. 1, second convolutional layer 106 of the second sub-QRNN 112 processes, as input, output from the preceding first pooling layer 104 of the first sub-QRNN 110. In contrast, first convolutional layer 102 of the first sub-QRNN 110 takes, as input, embedded vectors (e.g., word vectors, character vectors, phrase vectors,) mapped to a high-dimensional embedding space. Thus, in some implementations, varied input is provided to different sub-QRNNs of a stacked QRNN and/or to different components (e.g., convolutional layers, pooling layers) within a sub-QRNN.

Furthermore, QRNN 100 processes the output from a preceding sub-QRNN through a convolutional layer to produce an alternative representation of the preceding output. Then, the QRNN 100 processes the alternative representation through a pooling layer to produce an output. For example, in FIG. 1, the second sub-QRNN 112 uses the second convolutional layer 106 to convolve preceding output 114 from the first pooling layer 104 of the first sub-QRNN 110. The convolution produces an alternative representation 116, which is further processed by the second pooling layer 108 of the second sub-QRNN 112 to produce an output 118.

In some implementations, QRNN 100 also includes skip connections between the sub-QRNNs and/or between layers in a sub-QRNN. The skip connections, such as 120, 122, 124, concatenate output of a preceding layer with output of a current layer and provide the concatenation to a following layer as input. In one example of skip connections between layers of a sub-QRNN, skip connection 120 concatenates output 126 of the first convolutional layer 102 of the first sub-QRNN 110 with output 128 of the first pooling layer 104 of the first sub-QRNN 110. The concatenation is then provided as input to the second convolutional layer 106 of the second sub-QRNN 112. In one example of skip connections between sub-QRNNs, skip connection 122 concatenates the output 126 of the first convolutional layer 102 of the first sub-QRNN 110 with output 130 of the second convolutional layer 106 of the second sub-QRNN 112. The concatenation is then provided as input to the second pooling layer 108 of the second sub-QRNN 112. Likewise, skip connection 124 concatenates the output 128 of the first pooling layer 104 of the first sub-QRNN 110 with output 130 of the second convolutional layer 106 of the second sub-QRNN 112. The concatenation is then provided as input to the second pooling layer 108 of the second sub-QRNN 112.

For sequence classification tasks, QRNN 100 includes skip connections between every QRNN layer, which are referred to herein as “dense connections”. In one implementation, QRNN 100 includes dense connections between the input embeddings and every QRNN layer and between every pair of QRNN layers. This results in QRNN 100 concatenating each QRNN layer's input to its output along the feature dimension, before feeding the resulting state vectors into the next layer. The output of the last layer is then used as the overall encoding result.

QRNN Convolutional Layer—Timestep Parallelism

FIG. 2 shows one implementation of operation of a QRNN convolutional layer 200. FIG. 2 shows d-dimensional input vectors x₁, . . . , x₆, . . . , x_(n) representing n elements in an input sequence Xϵ

^(d×n). Input vectors x₁, . . . , x₆, . . . , x_(n) are respectively produced over n timesteps. In one implementation, the input sequence is a word-level input sequence with n words. In another implementation, the input sequence is a character-level input sequence with n characters. In yet another implementation, the input sequence is a phrase-level input sequence with n phrases. The input vectors x₁, . . . , x₆, . . . , x_(n) are mapped to a high-dimensional vector space, referred to herein as an “embedding space”. The embedding space is defined using an embedding matrix Eϵ

^(d×|v|), where v represents the size of the vocabulary. In implementations, the embedding space can be a word embedding space, a character embedding space, or a phrase embedding space. In some implementations, the input vectors x₁, . . . , x₆, . . . , x_(n) are initialized using pre-trained embedding models like GloVe and word2vec. In yet other implementations, the input vectors are based on one-hot encoding.

QRNN convolutional layer 200 performs parallel convolutions tom time series windows over the input vectors x₁, . . . , x₆, . . . , x_(n) with a bank of b filters to concurrently output a sequence Yϵ

^(ζd×m) of m convolutional vectors y₁, . . . , y₅, . . . , y_(m)·ζd is the dimensionality of each convolutional vector, where ζ identifies a dimensionality augmentation parameter. As used herein, “parallelism across the timestep or time series dimension” or “timestep or time series parallelism” refers to the QRNN convolutional layer 200 applying a convolutional filter bank in parallel to the input vectors x₁, . . . , x₆, . . . , x_(n) over m time series windows to concurrently produce m convolutional vectors y₁, . . . , y₅, . . . , y_(m).

In implementations, dimensionality of the concurrently outputted convolutional vectors y₁, . . . , y₅, . . . , y_(m) is augmented relative to dimensionality of the input vectors x₁, . . . , x₆, . . . , x_(n) in dependence upon a number of convolutional filters in the convolutional filter bank. Thus the dimensionality augmentation parameter ζ is proportionally dependent on the number of convolutional filters in the convolutional filter bank such that ζd=b. For example, if the dimensionality of the input vectors x₁, . . . , x₆, . . . , x_(n) is 100, i.e., d=100, and the convolutional filter bank contains 200 convolutional filters, i.e., b=200, then the dimensionality of the concurrently outputted convolutional vectors y₁, . . . , y₅, . . . , y_(m) is 200, i.e., ζd=200 and ζ=2. In other implementations, the convolutional filter bank is configured with varied number of convolutional filters, such that the dimensionality ζd of the concurrently outputted convolutional vectors is 300, 400, 500, 800, or any other number.

FIG. 3 depicts one implementation of a convolutional vector y_(m) 208 comprising an activation vector z_(m) 302, a forget gate vector f_(m) 304, an input gate vector i_(m) 306, and an output gate vector o_(m) 308. In implementations, a convolutional vector can include any combination of an activation vector and one or more gate vectors. For example, in one implementation, a convolutional vector comprises an activation vector and a forget gate vector. In another implementation, a convolutional vector comprises an activation vector, a forget gate vector, and input gate vector. In yet another implementation, a convolutional vector comprises an activation vector, a forget gate vector, and output gate vector.

In implementations, a number of gate vectors in a convolutional vector is configured in dependence upon the dimensionality ζd of the convolutional vector, such that ζd dimensions are proportionally split between an activation vector and one or more gate vectors of the convolutional vector. In one example, for convolutional vector y_(m) 208, if ζd=400, then the activation vector z_(m) 302, the forget gate vector f_(m) 304, the input gate vector i_(m) 306, and the output gate vector o_(m) 308, all have the same dimensionality d=100. In another example, for a convolutional vector of dimensionality ζ=200, the convolutional vector comprises an activation vector and only one gate vector (e.g., a forget gate vector), each of dimensionality d=100. In yet another example, for a convolutional vector of dimensionality ζd=300, the convolutional vector comprises an activation vector and two gate vectors (e.g., a forget gate vector and a output gate vector or a forget gate vector and an input gate vector), each of dimensionality d=100.

FIG. 4 is one implementation of multiple convolutional vectors y₁, . . . , y₅, . . . , y_(m), and comprising activation vectors and gate vectors, concurrently outputted by the QRNN convolutional layer 200. FIG. 4 shows a convolutional vector y₁ 202 generated by the QRNN convolutional layer 200 for the first time series window. Convolutional vector y₁ 202 comprises an activation vector z₁ 402, a forget gate vector f₁ 404, an input gate vector i₁ 406, and an output gate vector o₁ 408. Similarly, the QRNN convolutional layer 200 produces the convolutional vector y_(m) 208 for the m^(th) time series window.

In some implementations, in order to be useful for tasks that include prediction of the next element of an input sequence, the convolutional filters must not allow the computation for any given timestep to access information from future timesteps. That is, with filters of width k, each convolutional vector y_(t) depends only on input vectors x_(t−k+1) through x_(t). Such a convolutional operation is referred to herein as “masked convolution”. In one implementation, masked convolution is applied by padding the input to the left by the convolution's filter size minus one.

The concurrently outputted convolutional vectors y₁, . . . , y₅, . . . , y_(m) provide the activation vectors and the gate vectors that are used by a QRNN pooling layer to implement one or more QRNN pooling functions. In one implementation, prior to being used by a QRNN pooling layer, the activation vectors and the gate vectors are subjected to preprocessing. In one implementation, the preprocessing includes passing the activation vectors through a hyperbolic tangent nonlinearity activation (tan h). In one implementation, the preprocessing includes passing the gate vectors through an elementwise sigmoid nonlinearity activation (σ). For a QRNN pooling function that requires a forget gate vector f_(t) and an output gate vector o_(t) at each timestep window, the computations in a corresponding QRNN convolutional layer are defined by the following mathematical formulations:

Z=tan h(W _(z) *X)

F=σ(W _(f) *X)

O=σ(W _(o) *X)

where the activation vector W_(z), W_(f), and W_(o), each in

^(k×n×m), are convolutional filter banks and * denotes a masked convolution along the timestep dimension.

In one exemplary implementation, when the filter width of the convolutional filters is 2, the activation vector and the gate vectors represent LSTM-like gates and are defined by the following mathematical formulations:

z _(t)=tan h(w _(z) ¹ x _(t−1) +W _(z) ² x _(t))

f _(t)=σ(W _(f) ¹ x _(t−1) +W _(f) ² x _(t))

i _(t)=σ(W _(i) ¹ x _(t−1) +W _(i) ² x _(t))

o _(t)=σ(W _(o) ¹ x _(t−1) +W _(o) ² x _(t))

where the activation vector z_(t), the forget gate vector f_(t), the input gate vector i_(t), and the output gate vector o_(t) are concurrently produced by applying respective convolutional filter weight matrices W_(z) ¹, W_(z) ², W_(f) ¹, w_(f) ², W_(i) ¹, W_(i) ², W_(o) ¹, W_(o) ² to the input vectors x_(t−1) and x_(t).

In other implementations, convolutional filters of larger width are used to compute higher n-gram features at each timestep window. In implementations, larger widths are especially effective for character-level tasks.

QRNN Pooling Layer—QRNN Pooling Functions

QRNN pooling layers implement various QRNN pooling functions. QRNN pooling functions are controlled by one or more gate vectors provided by a corresponding QRNN convolutional layer. The gate vectors mix state vectors across timestep windows, while independently operating on each element of a state vector. In implementations, QRNN pooling functions are constructed from elementwise gates of an LSTM cell. In other implementations, QRNN pooling functions are constructed based on variants of an LSTM, such as no input gate (NIG) variant, no forget gate (NFG) variant, no output gate (NOG) variant, no input activation function (NIAF) variant, no output activation function (NOAF) variant, coupled input-forget gate (CIFG) variant, and full gate recurrent (FGR) variant. In yet other implementations, QRNN pooling functions are constructed based on operations of a gated recurrent unit (GRU), or any other type of RNN, or any other conventional or future-developed neural network.

f-Pooling

Consider the following mathematical formulation which defines one implementation of a QRNN pooling function, referred to herein as “f-pooling”, which uses a single gate vector:

c _(t) =f _(t)

c _(t−1)+(1−f _(t))

z _(t)  (1)

where,

-   -   c_(t) is the current state vector     -   f_(t) is the current forget state vector     -   c_(t−1) is the previous state vector     -   z_(t) is the current activation state vector     -   denotes elementwise multiplication or Hadamard Product

Regarding the state vector, a current state vector c_(t) is the consolidation of a current activation vector z_(t) with the past state vector c_(t−1). The current activation vector z_(t) is identified by a current convolutional vector y_(t), which is derived from a convolution over a current time series window of input vectors x_(t), . . . , x_(t+k−1), where k is the convolutional filter size or width. Anthropomorphically, the current state vector c_(t) knows the recipe of combining or mixing a currently convolved input vector window x_(t), . . . , x_(t+k−1) with the past state vector c_(t−1) so as to summarize the current input vector window x_(t), . . . , x_(t+k−1) in light of the contextual past. Thus the current activation vector z_(t) and the past state vector c_(t−1) are used to generate the current state vector c_(t) that includes aspects of the current input vector window x_(t), . . . , x_(t+k−1).

Regarding the forget gate vector, a current forget gate vector f_(t) makes an assessment of how much of the past state vector c_(t−1) is useful for the computation of the current state vector c_(t). In addition, the current forget gate vector f_(t) also provides an assessment of how much of the current activation vector z_(t) is useful for the computation of the current state vector c_(t).

fo-Pooling

In some implementations, a QRNN pooling function, which uses an output gate vector in addition to the forget gate vector, is referred to herein as “fo-pooling” and defined by the following mathematical formulations:

c _(t) =f _(t)

c _(t−1)+(1−f _(t))

z _(t)  (1)

h _(t) =o _(t)

c _(t)  (2)

where,

-   -   h_(t) is the current hidden state vector     -   o_(t) is the current output state vector     -   c_(t) is the current state vector     -   denotes elementwise multiplication or Hadamard Product

The current state vector c_(t) may contain information that is not necessarily required to be saved. A current output gate vector o_(t) makes an assessment regarding what parts of the current state vector c_(t) need to be exposed or present in a current hidden state vector h_(t).

ifo-Pooling

Consider the following mathematical formulation which defines one implementation of a QRNN pooling function, referred to herein as “ifo-pooling”, which uses multiple gate vectors:

c _(t) =f _(t)

c _(t−1) +i _(t)

z _(t)  (3)

where,

-   -   c_(t) is the current state vector     -   f_(t) is the current forget state vector     -   c_(t−1) is the previous state vector     -   i_(t) is the current input state vector     -   z_(t) is the current activation state vector     -   denotes elementwise multiplication or Hadamard Product

Regarding the input gate vector, for generating the current state vector c_(t), a current input gate vector i_(t) takes into account the importance of the current activation vector z_(t), and, by extension, also the importance of the current input vector window x_(t), . . . , x_(t+k−1). The input gate vector i_(t) is an indicator of how much of the current input is worth preserving and thus is used to gate the current state vector c_(t).

Therefore, anthropomorphically, mathematical formulation (3) involves: taking advice of the current forget gate vector f_(t) to determine how much of the past state vector c_(t−1) should be forgotten, taking advice of the current input gate vector i_(t) to determine how much of the current activation vector z_(t) should be taken into account, and summing the two results to produce the current state vector c_(t).

QRNN Pooling Layer—Feature Dimension Parallelism

A QRNN pooling layer calculates a state vector for each of the m time series windows using one or more QRNN pooling functions such as f-pooling, fo-pooling, and ifo-pooling. Each state vector is composed of a plurality of elements. Each element of a state vector is referred to herein as a “feature sum”. Each feature sum of a state vector is identified by a corresponding ordinal position in the state vector.

Consider the state vector sequence C depicted in FIG. 8. Sequence C comprises state vectors c₁, . . . , c_(m) In one example, a state vector c₁ 802 for the first time series window is composed of the following ordered set of 100 feature sums:

-   -   c₁ ¹, . . . , c₁ ¹⁰⁰         where the superscript identifies the ordinal position of a given         feature sum in a particular state vector and the subscript         identifies the particular state vector, and, by extension, also         the particular time series window.

Similarly, a state vector c_(m) 804 for the m^(th) time series window is also composed of an ordered set of 100 feature sums c_(m) ¹, . . . , c_(m) ¹⁰⁰.

The number of feature sums or elements in a state vector is proportionally dependent on the dimensionality d of the state vector. Thus, since state vector c₁ 802 has a dimensionality of 100, i.e., d=100, it has 100 feature sums. Also, the dimensionality d of a state vector is dependent on the dimensionality of the activation vectors and gate vectors used to calculate the state vector. In implementations, the activation vectors, the gate vectors, and the resulting state vectors share the same dimensionality d.

Typically, all the state vectors produced by a QRNN pooling layer for a given input sequence share the same dimensionality d. Thus, as shown in FIG. 8, state vectors c₁, . . . , c_(m) have the same number of feature sums or elements, with each feature sum being identified by a corresponding ordinal position within each state vector.

Like state vectors, the activation vectors and the gate vectors are also composed of a plurality of elements. Each element of an activation vector is referred to herein as a “feature value”. Similarly, each element of a gate vector is also referred to herein as a “feature value”. Each feature value of an activation vector is identified by a corresponding ordinal position in the activation vector. Similarly, each feature value of a gate vector is identified by a corresponding ordinal position in the gate vector.

Turning to FIG. 5, it shows an activation vector sequence Z of z₁, . . . , z_(m) activation vectors, a forget gate vector sequence F of f₁, . . . , f_(m) forget gate vectors, an input gate vector sequence I of i₁, . . . , i_(m) input gate vectors, and an output gate vector sequence O of o₁, . . . , o_(m) output gate vectors. As discussed above, the QRNN convolutional layer 200 concurrently outputs all the activation vectors and the gate vectors in the sequences Z, F, I, and O.

In one example, an activation vector z₁ 402 for the first time series window is composed of the following ordered set of 100 feature values:

-   -   z₁ ¹, . . . , z₁ ¹⁰⁰         where the superscript identifies the ordinal position of a given         feature value in a particular activation vector and the         subscript identifies the particular activation vector, and, by         extension, also the particular time series window.

Similarly, an activation vector z_(m) 302 for the m^(th) time series window is also composed of an ordered set of 100 feature values z_(m) ¹, . . . , z_(m) ¹⁰⁰.

In another example, a forget gate vector f₁ 404 for the first time series window is composed of the following ordered set of 100 feature values:

-   -   f₁ ¹, . . . , f₁ ¹⁰⁰         where the superscript identifies the ordinal position of a given         feature value in a particular forget gate vector and the         subscript identifies the particular forget gate vector, and, by         extension, also the particular time series window.

Similarly, a forget gate vector f_(m) 304 for the m^(th) time series window is also composed of an ordered set of 100 feature values f_(m) ¹, . . . , f_(m) ¹⁰⁰.

In yet another example, an input gate vector i₁ 406 for the first time series window is composed of the following ordered set of 100 feature values:

-   -   i₁ ¹, . . . , i₁ ¹⁰⁰         where the superscript identifies the ordinal position of a given         feature value in a particular input gate vector and the         subscript identifies the particular input gate vector, and, by         extension, also the particular time series window.

Similarly, an input gate vector i_(m) 306 for the m^(th) time series window is also composed of an ordered set of 100 feature values i_(m) ¹, . . . , i_(m) ¹⁰⁰.

In yet further example, an output gate vector o₁ 408 for the first time series window is composed of the following ordered set of 100 feature values:

-   -   o₁ ¹, . . . , o₁ ¹⁰⁰         where the superscript identifies the ordinal position of a given         feature value in a particular output gate vector and the         subscript identifies the particular output gate vector, and, by         extension, also the particular time series window.

Similarly, an output gate vector o_(m) 308 for the m^(th) time series window is also composed of an ordered set of 100 feature values o_(m) ¹, . . . , o_(m) ¹⁰⁰.

As used herein, “parallelism across the feature dimension” or “feature parallelism” refers to a QRNN pooling layer operating in parallel over feature values of a convolutional vector, i.e., over corresponding feature values in a respective activation vector and one or more gate vectors produced by the convolutional vector, to concurrently accumulate, in a state vector, an ordered set of feature sums. The accumulation of the feature sums can be based on one or more QRNN pooling functions such as f-pooling, fo-pooling, and ifo-pooling. Element-wise accumulation involves the feature values in the gate vectors serving as parameters that, respectively, apply element-wise by ordinal position to the feature values in the activation vector.

Consider one example of feature parallelism in FIG. 6, which is based on f-pooling implemented by a single-gate QRNN pooling layer 600. Note that the QRNN pooling layer 600 applies f-pooling “ordinal position-wise” using the following mathematical formulation:

$\begin{matrix} {{\underset{t = 1}{\overset{t = m}{\forall}}{\underset{j = 1}{\overset{j = d}{\forall}}\; c_{t}^{j}}} = {{f_{t}^{j} \cdot c_{t - 1}^{j}} + {\left( {1 - f_{t}^{j}} \right) \cdot z_{t}^{j}}}} & (4) \end{matrix}$

where, the pair for all symbols indicate operations over two dimensions of a matrix and

$\underset{t = 1}{\overset{t = m}{\forall}}$

denotes operation over successive time series windows

$\underset{j = 1}{\overset{j = d}{\forall}}$

denotes operations over ordinal positions, which are parallelizable

-   -   c_(t) ^(j) is the feature sum at the j ordinal position in the         current state vector c_(t)     -   f_(t) ^(j) is the feature value at the j ordinal position in the         current forget gate vector f_(t)     -   c_(t−1) ^(j) is the feature value at the j ordinal position in         the previous state vector c_(t−1)     -   z_(t) ^(j) is the feature value at the j ordinal position in the         current activation vector z_(t)     -   ● denotes multiplication

Mathematical formulation (4) involves computing a feature sum c_(t) ^(j) for a given ordinal position j in a state vector c_(t) for a current time series window t in dependence upon: a feature sum c_(t−1) ^(j) at the same ordinal position j in a state vector c_(t−1) for a previous time series window t−1, a feature value f_(t) ^(j) at the same ordinal position j in a forget gate vector f_(t) for a current time series window t, and a feature value z_(t) ^(j) at the same ordinal position j in a forget gate vector z_(t) for a current time series window t.

Therefore, anthropomorphically, in mathematical formulation (4), each feature value of a current forget gate vector controls ordinal position-wise accumulation of a respective feature value from a current activation vector and a respective feature sum from a previous state vector. Thus, in FIG. 6, feature sum c₁ ¹ is accumulated in dependence upon feature sum c₀ ¹ feature value f₁ ¹, and feature value z₁ ¹. Similarly, feature sum c₁ ² is accumulated in dependence upon feature sum c₀ ² feature value f₁ ², and feature value z₁ ². Likewise, feature sum c₁ ¹⁰⁰ is accumulated in dependence upon feature sum c₀ ¹⁰⁰, feature value f₁ ¹⁰⁰, and feature value z₁ ¹⁰⁰. In implementations, feature sums of a first state vector c₀ can be initialized to zero, or to pre-trained values, or to values dependent on the feature values of an activation vector.

Regarding feature parallelism, for the current time series state vector c_(t), the QRNN pooling layer 600 applies accumulators in parallel to concurrently accumulate feature sums for all the ordinal positions

$\underset{j = 1}{\overset{j = d}{\forall}}$

in the state vector c_(t) in accordance with the mathematical formulation (4). Thus, in FIG. 6, feature sums c₁ ¹, . . . , c₁ ¹⁰⁰ for state vector c₁ 802 for the first time series window are accumulated in parallel. Similarly, feature sums c₂ ¹, . . . , c₂ ¹⁰⁰ for state vector c₂ for the second time series window are accumulated in parallel. Likewise, feature sums c_(m) ¹, . . . , c_(m) ¹⁰⁰ for state vector c_(m) 804 for the m^(th) time series window are accumulated in parallel.

In addition, the QRNN pooling layer 600 sequentially outputs state vectors c_(m) ¹, . . . , c_(m) ¹⁰⁰ for each successive time series window

$\underset{t = 1}{\overset{t = m}{\forall}}$

among the m time series windows.

Consider another example of feature parallelism in FIG. 7, which is based on ifo-pooling implemented by a multi-gate pooling layer 700. Note that the QRNN pooling layer 700 applies ifo-pooling “ordinal position-wise” using the following mathematical formulation:

$\begin{matrix} {{\underset{t = 1}{\overset{t = m}{\forall}}{\underset{j = 1}{\overset{j = d}{\forall}}\; c_{t}^{j}}} = {{f_{t}^{j} \cdot c_{t - 1}^{j}} + {i_{t}^{j} \cdot z_{t}^{j}}}} & (5) \end{matrix}$

where, the pair for all symbols indicate operations over two dimensions of a matrix and

$\underset{t = 1}{\overset{t = m}{\forall}}$

denotes operation over successive time series windows

$\underset{j = 1}{\overset{j = d}{\forall}}$

denotes operations over ordinal positions, which are parallelizable

-   -   c_(t) ^(j) is the feature sum at the J ordinal position in the         current state vector c_(t)     -   f_(t) ^(j) is the feature value at the j ordinal position in the         current forget gate vector f_(t)     -   c_(t−1) ^(j) is the feature value at the J ordinal position in         the previous state vector c_(t−1)     -   i_(t) ^(j) is the feature value at the j ordinal position in the         current input gate vector i_(t)     -   z_(t) ^(j) is the feature value at the j ordinal position in the         current activation vector z_(t)     -   ● denotes multiplication

Mathematical formulation (5) involves computing a feature sum c_(t) ^(j) for a given ordinal position j in a state vector c_(t) for a current time series window t in dependence upon: a feature sum c_(t−1) ^(j) at the same ordinal position j in a state vector c_(t−1) for a previous time series window t−1, a feature value f_(t) ^(j) at the same ordinal position j in a forget gate vector f_(t) for a current time series window t, a feature value i_(t) ^(j) at the same ordinal position j in an input gate vector i_(t) for a current time series window t, and a feature value z_(t) ^(j) at the same ordinal position j in a forget gate vector z_(t) for a current time series window t.

Therefore, anthropomorphically, in mathematical formulation (5), each feature value of a current forget gate vector controls ordinal position-wise accumulation of a respective feature sum from a previous state vector, and each feature value of a current input gate vector controls, ordinal position-wise, accumulation of a respective feature value from a current activation vector. Thus, in FIG. 7, feature sum c₁ ¹ is accumulated in dependence upon feature sum c₀ ¹, feature value f₁ ¹, feature value i₁ ¹, and feature value z₁ ¹. Similarly, feature sum c₁ ² is accumulated in dependence upon feature sum c₀ ², feature value f₁ ², feature value i₁ ², and feature value z₁ ². Likewise, feature sum c₁ ¹⁰⁰ is accumulated in dependence upon feature sum c₀ ¹⁰⁰, feature value f₁ ¹⁰⁰, feature value i₁ ¹⁰⁰, and feature value z₁ ¹⁰⁰. In implementations feature sums of a first state vector c₀ can be initialized to zero, or to pre-trained values, or to values dependent on the feature values of an activation vector.

Regarding feature parallelism, for the current time series state vector c_(t), the QRNN pooling layer 700 applies accumulators in parallel to concurrently accumulate feature sums for all the ordinal positions

$\underset{j = 1}{\overset{j = d}{\forall}}$

in the state vector c_(t) in accordance with the mathematical formulation (5). Thus, in FIG. 7, feature sums c₁ ¹, . . . , c₁ ¹⁰⁰ or state vector c₁ 802 for the first time series window are accumulated in parallel. Similarly, feature sums c₂ ¹, . . . , c₂ ¹⁰⁰ for state vector c₂ for the second time series window are accumulated in parallel. Likewise, feature sums c_(m) ¹, . . . , c_(m) ¹⁰⁰ for state vector c_(m) 804 for the m^(th) time series window are accumulated in parallel.

In addition, the QRNN pooling layer 700 sequentially outputs state vectors c₁, . . . , c_(m) for each successive time series window

$\underset{t = 1}{\overset{t = m}{\forall}}$

among the m time series windows.

A single QRNN pooling layer thus performs an input-dependent pooling, followed by a gated linear combination of convolutional features. Although recurrent parts of the QRNN pooling functions are calculated by the QRNN pooling layers for each timestep in an input sequence, QRNN pooling layers' parallelism along feature dimensions means that, in practice, implementing the QRNN pooling functions over long input sequences requires a negligible amount of computation time.

In one implementation, the QRNN is regularized by requiring a random subset of feature sums at given ordinal positions in the state vector for the current time series window to replicate respective feature sums at the given ordinal positions in the state vector concurrently accumulated for the prior time series window. This is achieved by requiring respective feature values at the given ordinal positions in a forget gate vector for the current time series window to be unity.

QRNN Encoder-Decoder Model

FIG. 9 is one implementation of a QRNN encoder-decoder model 900 that increases computational efficiency in neural network sequence-to-sequence modeling. Model 900 includes a QRNN encoder and a QRNN decoder. The QRNN encoder comprises one or more encoder convolutional layers (like 902, 906) and one or more one encoder pooling layers (like 904, 908). At least one encoder convolutional layer (like 902) receives a time series of encoder input vectors and concurrently outputs encoded convolutional vectors for time series windows. Also, at least one encoder pooling layer (like 904 or 908) receives the encoded convolutional vectors for the time series windows, concurrently accumulates an ordered set of feature sums in an encoded state vector for a current time series window, and sequentially outputs an encoded state vector (like 922 a, 922 b, or 922 c) for each successive time series window among the time series windows.

The QRNN decoder comprises one or more decoder convolutional layers (like 914, 918) and one or more one decoder pooling layers (like 916, 920). At least one decoder convolutional layer (like 914) receives a time series of decoder input vectors and concurrently outputs decoded convolutional vectors for time series windows. At least one decoder pooling layer (like 916 or 920) receives the decoded convolutional vectors (like 915 a, 915 b, 915 c) for the time series windows respectively concatenated with an encoded state vector (like 910 or 912) outputted by an encoder pooling layer (like 904 or 908) for a final time series window, concurrently accumulates an ordered set of feature sums in a decoded state vector for a current time series window, and sequentially outputs a decoded state vector (like 924 a, 924 b, or 924 c) for each successive time series window among the time series windows. Thus, the output of each decoder QRNN layer's convolution functions is supplemented at every timestep with the final encoder hidden state. This is accomplished by adding the result of the convolution for layer l (e.g., W_(z) ^(l)*X^(l), in

^(T×m)) with broadcasting to a linearly projected copy of layer l's last encoder state (e.g., V_(z) ^(l){tilde over (h)}_(T) ^(l), in

^(m)) (like 910 or 912).

Activation vectors and the gate vectors for the QRNN encoder-decoder model 900 are defined by the following mathematical formulation:

Z ^(l)=tan h(W _(z) ^(l) *X ^(l) +V _(z) ^(l) {tilde over (h)} _(T) ^(l))

F ^(l)=σ(W _(f) ^(l) *X ^(l) +V _(f) ^(l) {tilde over (h)} _(T) ^(l))

O ^(l)=σ(W _(o) ^(l) *X ^(l) +V _(o) ^(l) {tilde over (h)} _(T) ^(l))

where the tilde denotes that {tilde over (h)} is an encoder variable.

Then, a state comparator calculates linguistic similarity (e.g., using dot product or inner product or bilinear product) between the encoded state vectors (like 922 a, 922 b, or 922 c) and the decoded state vectors (like 924 a, 924 b, or 924 c) to produce an affinity matrix 926 with encoding-wise and decoding-wise axes. Next, an exponential normalizer 928, such as softmax, normalizes the affinity matrix 926 encoding-wise to produce respective encoding-to-decoding attention weights α_(st), defined as:

α_(st)=softmax(c _(t) ^(L)

{tilde over (h)} _(s) ^(L))

Then, an encoding mixer respectively combines the encoded state vectors (like 922 a, 922 b, or 922 c) with the encoding-to-decoding attention weights to generate respective contextual summaries k_(t) of the encoded state vectors, defined as:

$k_{t} = {\sum\limits_{s}{\alpha_{st}{\overset{\sim}{h}}_{s}^{L}}}$

Finally, an attention encoder respectively combines the decoded state vectors (like 924 a, 924 b, or 924 c) with the respective contextual summaries of the encoded state vectors to produce an attention encoding for each of the time series windows. In one implementation, the attention encoder is a multilayer perceptron that projects a concatenation of the decoded state vectors and respective contextual summaries of the encoded state vectors into non-linear projections to produce an attention encoding for each of the time series windows.

In some implementations, the encoded state vectors (like 922 a, 922 b, or 922 c) are respectively multiplied by output gate vectors of the encoded convolutional vectors to produce respective encoded hidden state vectors. In such implementations, the state comparator calculates linguistic similarity (e.g., using dot product or inner product or bilinear product) between the encoded hidden state vectors and the decoded state vectors to produce an affinity matrix with encoding-wise and decoding-wise axes. Also, in such implementations, the encoding mixer respectively combines the encoded hidden state vectors with the encoding-to-decoding attention weights to generate respective contextual summaries of the encoded hidden state vectors. Further, in such implementations, the attention encoder respectively combines the decoded state vectors with the respective contextual summaries of the encoded hidden state vectors, and further multiplies the combinations with respective output gate vectors of the decoded convolutional vectors to produce an attention encoding for each of the time series windows. In one implementation, the attention encoder is a multilayer perceptron that projects a concatenation of the decoded state vectors and respective contextual summaries of the encoded hidden state vectors into non-linear projections, and further multiplies the non-linear projections 930 with respective output gate vectors 932 of the decoded convolutional vectors to produce an attention encoding for each of the time series windows, defined as:

h _(t) ^(L) =o _(t)

(W _(k) k _(t) +W _(c) c _(t) ^(L))

where L is the last layer.

While the first step of the attention procedure is quadratic in the sequence length, in practice it takes significantly less computation time than the model's linear and convolutional layers due to the simple and highly parallel dot-product scoring function.

Other implementations of the technology disclosed include using normalizers different than, in addition to, and/or in combination with the exponential normalizer. Some examples include sigmoid based normalizers (e.g., multiclass sigmoid, piecewise ramp), hyperbolic tangent based normalizers, rectified linear unit (ReLU) based normalizers, identify based normalizers, logistic based normalizers, sine based normalizers, cosine based normalizers, unit sum based normalizers, and step based normalizers. Other examples include hierarchical softmax, differentiated softmax, importance sampling, noise contrastive estimation, negative sampling, gated softmax spherical softmax, Taylor softmax, and sparsemax. In yet other implementations, any other conventional or future-developed normalizer can be used.

Experimental Results

QRNN outperforms LSTM-based models of equal state vector size on three different natural language processing (NLP) tasks, namely, document-level sentiment classification, language modeling, and character-based neural network machine translation, while dramatically improving computation speed.

FIG. 10 is a table that shows accuracy comparison of the QRNN on sentiment classification task for a popular document-level sentiment classification benchmark, the IMDb movie review dataset. The dataset consists of a balanced sample of 25,000 positive and 25,000 negative reviews, divided into equal-size train and test sets, with an average document length of 231 words. In one implementation, a QRNN having a four-layer densely connected architecture with 256 units per layer and word vectors initialized using 300-dimensional cased GloVe embeddings achieves best performance on a held-out development.

FIG. 11 shows one implementation of visualization of hidden state vectors of the final QRNN layer on part of an example from the IMDb dataset, with timesteps along the vertical axis. Even without any post-processing, changes in the hidden state are visible and interpretable in regards to the input. This is a consequence of the elementwise nature of the recurrent pooling function, which delays direct interaction between different channels of the hidden state until the computation of the next QRNN layer.

In FIG. 11, colors denote neuron activations. After an initial positive statement “This movie is simply gorgeous” (off graph at timestep 9), timestep 117 triggers a reset of most hidden states due to the phrase “not exactly a bad story” (soon after “main weakness is its story”). Only at timestep 158, after “I recommend this movie to everyone, even if you've never played the game”, do the hidden units recover.

FIG. 12 depicts a table that shows accuracy comparison of the QRNN on language modeling task. The experiment uses a standard preprocessed version of the Penn Treebank (PTB). FIG. 12 shows single model perplexity on validation and test sets for the Penn Treebank language modeling task. Lower is better. “Medium” refers to a two-layer network with 640 or 650 hidden units per layer. All QRNN models include dropout of 0.5 on embeddings and between layers, in some implementations. MC refers to Monte Carlo dropout averaging at test time.

As shown in FIG. 12, the QRNN strongly outperforms different types of LSTMs. This is due to the efficient computational capacity that the QRNN's pooling layer has relative to the LSTM's recurrent weights, which provide structural regularization over the recurrence.

FIG. 13 is a table that shows accuracy comparison of the QRNN on language translation task. The QRNN encoder-decoder model is evaluated on a challenging neural network machine translation task, IWSLT German-English spoken-domain translation, applying fully character-level segmentation. This dataset consists of 209,772 sentence pairs of parallel training data from transcribed TED and TEDx presentations, with a mean sentence length of 103 characters for German and 93 for English.

The QRNN encoder-decoder model achieves best performance on a development set (TED.tst2013) using a four-layer encoder-decoder QRNN with 320 units per layer, no dropout or L2 regularization, and gradient rescaling to a maximum magnitude of 5. FIG. 13 shows that the QRNN encoder-decoder model outperforms the character-level LSTM, almost matching the performance of a word-level attentional baseline.

FIG. 14 depicts charts that show training speed and inference speed of the QRNN. In FIG. 14, the training speed for two-layer 640-unit PTB LM on a batch of 20 examples of 105 timesteps is shown on the left. “RNN” and “softmax” include the forward and backward times, while “optimization overhead” includes gradient clipping, L2 regularization, and SGD computations. On the right, FIG. 14 shows the inference speed advantage of a 320-unit QRNN layer over an equal-sized cuDNN LSTM layer for data with the given batch size and sequence length. Training results are similar.

Sample Code

The following sample code shows one implementation of the QRNN 100:

from chainer import cuda, Function, Variable, Chain import chainer.links as L import chainer.functions as F import numpy as np THREADS_PER_BLOCK = 32 class STRNNFunction(Function): def forward_gpu(self, inputs): f, z, hinit = inputs b, t, c = f.shape assert c % THREADS_PER_BLOCK == 0 self.h = cuda.cupy.zeros((b, t + 1, c), dtype=np.float32) self.h[:, 0, :] = hinit cuda.raw(‘“ #define THREADS_PER_BLOCK 32 extern “C” _(——)global_(——) void strnn_fwd( const CArray<float, 3> f, const CArray<float, 3> z, CArray<float, 3> h) { int index[3]; const int t_size = f.shape( )[1]; index[0] = blockIdx.x; index[1] = 0; index[2] = blockIdx.y * THREADS_PER_BLOCK + threadIdx.x; float prev_h = h[index]; for (int i = 0; i < t_size; i++){ index[1] = i; const float ft = f[index]; const float zt = z [index]; index[1] = i + 1; float &ht = h[index]; prev_h = prev_h * ft + zt; ht = prev_h; } }’”, ‘strnn_fwd’)( (b, c // THREADS_PER_BLOCK), (THREADS_PER_BLOCK,), (f, z, self.h)) return self.h[:, 1:, :], def backward_gpu(self, inputs, grads): f, z = inputs[:2] gh, = grads b, t, c = f.shape gz = cuda.cupy.zeros_like(gh) cuda.raw(‘“ #define THREADS_PER_BLOCK 32 extern “C” _(——)global_(——) void strnn_back( const CArray<float, 3> f, const CArray<float, 3> gh, CArray<float, 3> gz) { int index[3]; const int t_size = f.shape( )[1]; index[0] = blockIdx.x; index[2] = blockIdx.y * THREADS_PER_BLOCK + threadIdx.x; index[1] = t_size − 1; float &gz_last = gz[index]; gz_last = gh[index]; float prev_gz = gz_last; for (int i = t_size − 1; i > 0; i−−){ index[1] = i; const float ft = f[index]; index[1] = i − 1; const float ght = gh[index]; float &gzt = gz[index]; prev_gz = prev_gz * ft + ght; gzt = prev_gz; } }’”, ‘strnn_back’)( (b, c // THREADS_PER_BLOCK), (THREADS_PER_BLOCK,), (f, gh, gz)) gf = self.h[:, :−1, :] * gz ghinit = f[:, 0, :] * gz[:, 0, :] return gf, gz, ghinit def strnn(f, z, h0): return STRNNFunction( )(f, z, h0) def attention sum(encoding, query): alpha = F.softmax(F.batch_matmul(encoding, query, transb=True)) alpha, encoding = F.broadcast(alpha[:, :, :, None], encoding[:, :, None, :]) return F.sum(alpha * encoding, axis=1) class Linear(L.Linear): def_(——)call_(——)(self, x): shape = x. shape if len(shape) == 3: x = F.reshape(x, (−1, shape[2])) y = super( )._(——)call_(——)(self, x) if len(shape) == 3: y = F.reshape(y, shape) return y class QRNNLayer(Chain): def_(——)init_(——)(self, in_size, out_size, kernel_size=2, attention=False,  decoder=False): if kernel_size == 1: super( )._(——)init_(——)(W=Linear(in_size, 3 * out_size)) elif kernel_size == 2: super( )._(——)init_(——)(W=Linear(in_size, 3 * out_size, nobias=True), V=Linear(in_size, 3 * out_size)) else: super( )._(——)init_(——)( conv=L.ConvolutionND(1, in_size, 3 * out_size, kernel_size, stride=1, pad=kernel_size − 1)) if attention: self.add_link(‘U’, Linear(out_size, 3 * in_size)) self.add_link(‘o’, Linear(2 * out_size, out_size)) self.in_size, self.size, self.attention = in_size, out_size, attention self.kernel_size = kernel_size def pre(self, x): dims = len(x.shape) − 1 if self.kernel_size == 1: ret = self.W(x) elif self.kernel_size == 2: if dims == 2: xprev = Variable( self.xp.zeros((selfbatch_size, 1, self.in_size), dtype=np.float32), volatile=‘AUTO’) xtminus1 = F.concat((xprev, x[:, :−1, :]), axis=1) else: xtminus1 = self.x ret = self.W(x) + self.V(xtminus1) else: ret = F.swapaxes(self.conv( F.swapaxes(x, 1, 2))[:, :, :x.shape[2]], 1, 2) if not self.attention: return ret if dims == 1: enc = self.encoding[:, −1, :] else: enc = self.encoding[:, −1:, :] return sum(F.broadcast(self.U(enc), ret)) def init(self, encoder_c=None, encoder_h=None): self.encoding = encoder_c self.c, self.x = None, None if self.encoding is not None: self.batch_size = self.encoding.shape[0] if not self.attention: self.c = self.encoding[:, −1, :] if self.c is None or self.c. shape[0] < self.batch_size: self.c = Variable(self.xp.zeros((self.batch_size, self.size), dtype=np.float32), volatile=‘AUTO’) if self.x is None or self.x.shape[0] < self.batch_size: self.x = Variable(self.xp.zeros((self.batch_size, self.in_size), dtype=np.float32), volatile=‘AUTO’) def_(——)call_(——)(self, x): if not hasattr(self, ‘encoding’) or self.encoding is None: self.batch_size = x.shape[0] self.init( ) dims = len(x.shape) − 1 f, z, o = F.split_axis(self.pre(x), 3, axis=dims) f = F.sigmoid(f) z = (1 − f) * F.tanh(z) o = F.sigmoid(o) if dims == 2: self.c = strnn(f, z, self.c[:self.batch_size]) else: self.c = f * self.c + z if self.attention: context = attention_sum(self.encoding, self.c) self.h = o * self.o(F.concat((self.c, context), axis=dims)) else: self.h = self.c * o self.x = x return self.h def get_state(self): return F.concat((self.x, self.c, self.h), axis=1) def set_state(self, state): self.x, self.c, self.h = F.split_axis( state, (self.in_size, self.in_size + self.size), axis=1) state = property(get_state, set_state)

Computer System

FIG. 15 is a simplified block diagram of a computer system 1500 that can be used to implement the QRNN 100. Computer system 1500 typically includes one or more CPU processors 1520 that communicate with a number of peripheral devices via bus subsystem 1532. These peripheral devices can include a memory subsystem 1512 including, for example, memory devices and a file storage subsystem 1518, user interface input devices 1530, user interface output devices 1524, a network interface subsystem 1522, and a GPU 1526 with multiple GPU processing cores or GPU processors 1528. The input and output devices allow user interaction with computer system 1500. Network interface subsystem 1522 provides an interface to outside networks, including an interface to corresponding interface devices in other computer systems.

The convolutional and pooling operations of the QRNN 100 are performed by the GPU processing cores 1528, according to some implementations. In one implementation, the accumulators, which operate in parallel to concurrently output feature sums of a state vector, are simultaneously run on individual GPU processing cores 1528. Thus each GPU processor calculates a feature sum for a given ordinal position in a state vector, and a set of GPU processors execute in parallel to concurrently calculate all the feature sums for all the ordinal positions of the vector. Accordingly, the QRNN 100 improves the computational efficiency of the GPU 1526.

User interface input devices 1530 or clients or client devices can include a keyboard; pointing devices such as a mouse, trackball, touchpad, or graphics tablet; a scanner; a touch screen incorporated into the display; audio input devices such as voice recognition systems and microphones; and other types of input devices. In general, use of the term “input device” is intended to include all possible types of devices and ways to input information into computer system 1500.

User interface output devices 1524 can include a display subsystem, a printer, a fax machine, or non-visual displays such as audio output devices. The display subsystem can include a cathode ray tube (CRT), a flat-panel device such as a liquid crystal display (LCD), a projection device, or some other mechanism for creating a visible image. The display subsystem can also provide a non-visual display such as audio output devices. In general, use of the term “output device” is intended to include all possible types of devices and ways to output information from computer system 1500 to the user or to another machine or computer system.

Storage subsystem 1510 stores programming and data constructs that provide the functionality of some or all of the modules and methods described herein. These software modules are generally executed by CPU processors 1520 alone or in combination with other processors like GPU processors 1528.

Memory subsystem 1512 in the storage subsystem can include a number of memories including a main random access memory (RAM) 1516 for storage of instructions and data during program execution and a read only memory (ROM) 1514 in which fixed instructions are stored. A file storage subsystem 1518 can provide persistent storage for program and data files, and can include a hard disk drive, a floppy disk drive along with associated removable media, a CD-ROM drive, an optical drive, or removable media cartridges. The modules implementing the functionality of certain implementations can be stored by file storage subsystem 1518 or the memory subsystem 1512, or in other machines accessible by the processor.

Bus subsystem 1532 provides a mechanism for letting the various components and subsystems of computer system 1500 communicate with each other as intended. Although bus subsystem 1532 is shown schematically as a single bus, alternative implementations of the bus subsystem can use multiple busses. In some implementations, an application server (not shown) can be a framework that allows the applications of computer system 1500 to run, such as the hardware and/or software, e.g., the operating system.

Computer system 1500 itself can be of varying types including a personal computer, a portable computer, a workstation, a computer terminal, a network computer, a television, a mainframe, a server farm, a widely-distributed set of loosely networked computers, or any other data processing system or user device. Due to the ever-changing nature of computers and networks, the description of computer system 1500 depicted in FIG. 15 is intended only as a specific example for purposes of illustrating the preferred embodiments of the present invention. Many other configurations of computer system 1500 are possible having more or less components than the computer system depicted in FIG. 15.

The preceding description is presented to enable the making and use of the technology disclosed. Various modifications to the disclosed implementations will be apparent, and the general principles defined herein may be applied to other implementations and applications without departing from the spirit and scope of the technology disclosed. Thus, the technology disclosed is not intended to be limited to the implementations shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein. The scope of the technology disclosed is defined by the appended claims. 

What is claimed is:
 1. A quasi-recurrent neural network (QRNN) system that increases computational efficiency in neural network sequence modeling, the system comprising: a convolutional layer that receives a time series of input vectors, applies a convolutional filter bank in parallel to time series windows over the input vectors, and concurrently outputs convolutional vectors for the time series windows, each of the convolution vectors comprising feature values in an activation vector and in one or more gate vectors, and the feature values in the gate vectors are parameters that, respectively, apply element-wise by ordinal position to the feature values in the activation vector; and a pooling layer that receives the convolutional vectors for the time series windows, and operates in parallel over feature values of a convolutional vector to concurrently accumulate ordinal position-wise, in a state vector for a current time series window, an ordered set of feature sums in dependence upon a feature value at a given ordinal position in an activation vector outputted for the current time series window, one or more feature values at the given ordinal position in one or more gate vectors outputted for the current time series window, and a feature sum at the given ordinal position in a state vector accumulated for a prior time series window; and sequentially outputs a state vector for each successive time series window among the time series windows.
 2. The system of claim 1, wherein dimensionality of the convolutional vectors is augmented relative to dimensionality of the input vectors in dependence upon a number of convolutional filters in the convolutional filter bank.
 3. The system of claim 1, wherein the input vectors represent elements of an input sequence, and wherein the pooling layer encodes order and context information of the elements in the state vectors.
 4. The system of claim 3, wherein the input sequence is a word-level sequence.
 5. The system of claim 3, wherein the input sequence is a character-level sequence.
 6. The system of claim 1, wherein the gate vector is a forget gate vector, and wherein the pooling layer uses a forget gate vector for a current time series window to control accumulation of information from a state vector accumulated for a prior time series window and information from an activation vector for the current time series window.
 7. The system of claim 1, wherein the gate vector is an input gate vector, and wherein the pooling layer uses an input gate vector for a current time series window to control accumulation of information from an activation vector for the current time series window.
 8. The system of claim 1, wherein the gate vector is an output gate vector, and wherein the pooling layer uses an output gate vector for a current time series window to control accumulation of information from a state vector for the current time series window.
 9. The system of claim 1, further configured to comprise a plurality of sub-QRNNs arranged in a sequence from lowest to highest, each sub-QRNN comprising at least one convolutional layer and at least one pooling layer.
 10. The system of claim 9, wherein the sub-QRNNs are configured to: receive as input a preceding output generated by a preceding sub-QRNN in the sequence; process the preceding output through the convolutional layer to produce an alternative representation of the preceding output; and process the alternative representation through the pooling layer to produce an output.
 11. The system of claim 10, further configured to include skip connections between the sub-QRNNs and between layers in the sub-QRNN, wherein the skip connections concatenate output of a preceding layer with output of a current layer and provide the concatenation to a following layer as input.
 12. The system of claim 1, further configured to train convolutional filters in the convolutional filter bank using a sequence task.
 13. The system of claim 12, wherein the sequence task is language modeling.
 14. The system of claim 12, wherein the sequence task is sentiment classification.
 15. The system of claim 12, wherein the sequence task is document classification.
 16. The system of claim 12, wherein the sequence task is word-level machine translation.
 17. The system of claim 12, wherein the sequence task is character-level machine translation.
 18. The system of claim 1, further configured to regularize the QRNN by: requiring a random subset of feature sums at given ordinal positions in the state vector for the current time series window to replicate respective feature sums at the given ordinal positions in the state vector concurrently accumulated for the prior time series window, including requiring respective feature values at the given ordinal positions in a forget gate vector for the current time series window to be unity.
 19. A quasi-recurrent neural network (QRNN) system that increases computational efficiency in neural network sequence modeling, the system comprising: a convolutional layer, running on numerous processing cores, that receives a time series of input vectors, applies a convolutional filter bank in parallel to time series windows over the input vectors, and concurrently outputs convolutional vectors for the time series windows, each of the convolution vectors comprising feature values in an activation vector and in one or more gate vectors, the gate vectors including a forget gate vector, and the feature values in the gate vectors are parameters that, respectively, apply element-wise by ordinal position to the feature values in the activation vector; and a pooling layer, running on numerous processing cores, that receives the convolutional vectors for the time series windows, and applies accumulators in parallel to respective feature values of a convolutional vector, to calculate a state vector for each successive timestep among the time series windows; and at each timestep, for respective ordinal positions in an activation vector and one or more gate vectors of the convolutional vector, an accumulator begins with a feature sum at a given ordinal position in a state vector from a prior timestep, if any, multiplied by a respective feature value at the given ordinal position in the forget gate vector for a current timestep, adds an evaluation of a respective feature value at the given ordinal position in the activation vector for the current timestep against one or more respective feature values at the given ordinal position in the gate vectors for the current timestep, and outputs a state vector for the current timestep that combines results of the accumulators across all of the respective ordinal positions.
 20. The system of claim 19, wherein the pooling layer uses the forget gate vector for the current timestep to control accumulation of information from the activation vector for the current timestep.
 21. The system of claim 19, wherein the gate vectors include an input gate vector, and wherein the pooling layer uses an input gate vector for the current timestep to control accumulation of information from the activation vector for the current timestep.
 22. The system of claim 19, wherein the gate vectors include an output gate vector, and wherein the pooling layer uses an output gate vector for the current timestep to control accumulation of information from the state vector for the current timestep.
 23. A method that increases computational efficiency in neural network sequence modeling, the method including: receiving a time series of input vectors; applying a convolutional filter bank in parallel to time series windows over the input vectors; concurrently outputting convolutional vectors for the time series windows, each of the convolution vectors comprising feature values in an activation vector and in one or more gate vectors, and the feature values in the gate vectors are parameters that, respectively, apply element-wise by ordinal position to the feature values in the activation vector; operating in parallel over feature values of a convolutional vector to concurrently accumulate ordinal position-wise, in a state vector for a current time series window, an ordered set of feature sums in dependence upon a feature value at a given ordinal position in an activation vector outputted for the current time series window, one or more feature values at the given ordinal position in one or more gate vectors outputted for the current time series window, and a feature sum at the given ordinal position in a state vector accumulated for a prior time series window; and sequentially outputting a state vector for each successive time series window among the time series windows.
 24. A quasi-recurrent neural network (QRNN) system that increases computational efficiency in neural network sequence modeling, the system comprising: a convolutional layer that receives a time series of input vectors and concurrently outputs convolutional vectors for time series windows; and a pooling layer that receives the convolutional vectors for the time series windows and concurrently accumulates an ordered set of feature values in a state vector for a current time series window, and sequentially outputs a state vector for each successive time series window among the time series windows.
 25. A non-transitory computer readable storage medium impressed with computer program instructions, the instructions, when executed on a processor, implement the system of claim
 1. 26. A non-transitory computer readable storage medium impressed with computer program instructions, the instructions, when executed on a processor, implement the system of claim
 24. 